Non-linear Transport in Multifold Semimetals Reveals Third-Order Response Functions for Enhanced Electronic Structure Probing

Understanding how electrons move through materials is fundamental to developing new technologies, but interpreting these movements can be complex. Andrea Kouta Dagnino, Xiaoxiong Liu, and Titus Neupert, from the University of Z ̈urich and Southern University of Science and Technology, investigate this challenge by exploring electron transport in a recently discovered class of materials called multifold semimetals. Their work establishes a comprehensive theoretical framework for understanding how electrons respond to electric fields, even very strong ones, within these materials. This achievement allows scientists to predict and potentially control the behaviour of electrons based on the material’s symmetry and electronic structure, paving the way for novel applications in nonlinear valley-tronics, a field that manipulates electron properties for advanced electronic devices.

By analysing both linear and non-linear responses, researchers can draw definite conclusions, as demonstrated by studies of the circular photogalvanic effect in Weyl semimetals. The team derives complete expressions for intrinsic transport response functions, extending to third order in the applied electric field, within the framework of Boltzmann theory, combining information about quantum geometry and band dispersion. They discuss the responses for multifold fermions at high-symmetry momenta in time-reversal symmetric crystals, and how symmetry constraints reduce these responses, exemplifying the cases of space groups 213 and 199, which realise different multifold fermions.

Nonlinear Optics and Topological Fermion Classification

This supplementary material details extensive calculations and classifications related to non-linear optical conductivities and topological fermions in materials, providing a comprehensive framework for understanding these phenomena and offering practical tools for researchers. The research investigates non-linear optical conductivities, specifically second and third-order responses, crucial for understanding non-linear optical phenomena, and classifies multi-fold fermions, including 3-fold, 4-fold, 6-fold, and 8-fold varieties, in materials with spin-orbit coupling and time-reversal symmetry, relating these to exotic electronic states and potential applications in quantum technologies. The work connects Fermi surface integrals to measurable conductivities, providing a pathway from theoretical calculations to experimental verification. A central component of this material is the provision of explicit formulas for calculating various conductivities, including contributions from the Drude model, Berry curvature, and polarization effects, expressed as integrals over the Fermi surface, allowing researchers to calculate conductivities given a material’s band structure and Fermi surface.

The research also classifies multi-fold fermions based on their degeneracy and compatibility with specific space groups and crystal point groups, using the little co-group, which describes symmetry operations that leave the relevant momentum point invariant. Comprehensive tables list the space groups, crystal point groups, momentum points, and little co-groups for each type of multi-fold fermion. This work provides practical calculations for non-linear optical conductivities from first principles, given a material’s band structure, and a roadmap for discovering materials that host exotic electronic states, emphasizing the crucial role of symmetry in determining the existence and properties of these fermions and highlighting their potential connection to quantum technologies. This material is intended for researchers in condensed matter physics, materials science, and related fields, requiring a strong background in band theory, symmetry analysis, and non-linear optics.

Quantum Geometry Dictates Nonlinear Charge Transport

This research presents a comprehensive theoretical framework for understanding how quantum geometry and band dispersion influence charge transport in quantum materials. The team successfully derived complete expressions for intrinsic transport response functions, extending to third order in the applied electric field, using Boltzmann theory, revealing how symmetry constraints impact these responses and demonstrating the potential to differentiate between various multifold fermions through their non-linear responses. Detailed analysis of materials belonging to space groups 213 and 199 exemplifies this differential addressing, paving the way for novel nonlinear valley-tronics. The findings establish a strong connection between quantum geometry, band structure, and measurable charge transport properties, offering a pathway to isolate and study quantum geometric effects in experiments. While acknowledging the difficulty of experimentally isolating these effects, the researchers highlight the potential of their theoretical framework to guide the design of materials and experiments specifically tailored to reveal the influence of quantum geometry.